Chapter 18, Problem 18.77P

CALC (a) Explain why in a gas of N molecules, the number of molecules having speeds in the finite interval υ to υ + Δυ is $\Delta N={\displaystyle {\int }_{\upsilon }^{\upsilon +\Delta \upsilon }f(\upsilon )d\upsilon }$. (b) If Δυ is small, then f(υ) is approximately constant over the interval and ΔN ≈ Nf(υ)Δυ. For oxygen gas (O₂, molar mass 32.0 g/mol) at T = 300 K, use this approximation to calculate the number of molecules with speeds within Δυ = 20 m/s of υ_mp. Express your answer as a multiple of N. (c) Repeat part (b) for speeds within Δυ = 20 m/s of 7υ_mp. (d) Repeat parts (b) and (c) for a temperature of 600 K. (e) Repeat parts (b) and (c) for a temperature of 150 K. (f) What do your results tell you about the shape of the distribution as a function of temperature? Do your conclusions agree with what is shown in Fig. 18.23?